Correlated Features Simulation
We will first investigate how various feature importance methods treat correlated variables under different simulation scenarios.
n <- 500
p <- 10
beta <- 1
noise_sd <- 1
data_ls <- list()
vimp_ls <- list()
fit_ls <- list()
# case 1: independent features
X <- as.data.frame(matrix(rnorm(n * p), n, p))
y <- X[, 1] * beta + X[, 2] * beta + rnorm(n, sd = noise_sd)
data_ls[["Independent Features"]] <- data.frame(y = y, X)
# case 2: correlated non-signal features
p_cor <- 100
rho <- 0.9
sig <- matrix(rho, p_cor, p_cor)
X_cor <- MASS::mvrnorm(n, mu = rep(0, p_cor), Sigma = sig)
data_ls[["Correlated Non-signal Features"]] <- dplyr::bind_cols(
data.frame(y = y, X),
as.data.frame(X_cor) |> dplyr::rename_with(~ paste0("corr", .x))
)
# case 3: correlated signal features (one signal)
sig <- matrix(rho, p_cor + 1, p_cor + 1)
X_cor <- MASS::mvrnorm(n, mu = rep(0, p_cor + 1), Sigma = sig)
X[, 1] <- X_cor[, 1]
X_cor <- X_cor[, -1]
y <- X[, 1] * beta + X[, 2] * beta + rnorm(n, sd = noise_sd)
data_ls[["Correlated Signal Features (1 signal)"]] <- dplyr::bind_cols(
data.frame(y = y, X),
as.data.frame(X_cor) |> dplyr::rename_with(~ paste0("corr", .x))
)
# case 4: correlated signal features (many signal)
y <- X[, 1] * beta + X[, 2] * beta + rowSums(X_cor[, 1:4] * beta) + rnorm(n, sd = noise_sd)
data_ls[["Correlated Signal Features (many signal)"]] <- dplyr::bind_cols(
data.frame(y = y, X),
as.data.frame(X_cor) |> dplyr::rename_with(~ paste0("corr", .x))
)
for (sim_name in names(data_ls)) {
cat(sprintf("\n\n## %s {.tabset .tabset-pills .tabset-square}\n\n", sim_name))
data <- data_ls[[sim_name]]
y <- data |>
dplyr::pull(y)
X <- data |>
dplyr::select(-y)
# linear regression
lm_fit <- lm(y ~ ., data = data)
lm_vimp_df <- tibble::tibble(
var = names(summary(lm_fit)$coefficients[-1, 1]),
vimp = summary(lm_fit)$coefficients[-1, 1],
se = summary(lm_fit)$coefficients[-1, 2]
)
# LASSO regression
lasso_fit <- glmnet::cv.glmnet(
x = as.matrix(X),
y = y,
alpha = 1,
nfolds = 5
)
lasso_vimp_df <- tibble::tibble(
var = rownames(coef(lasso_fit, s = "lambda.min"))[-1],
vimp = as.matrix(coef(lasso_fit, s = "lambda.min"))[-1]
)
# ridge regression
ridge_fit <- glmnet::cv.glmnet(
x = as.matrix(X),
y = y,
alpha = 0,
nfolds = 5
)
ridge_vimp_df <- tibble::tibble(
var = rownames(coef(ridge_fit, s = "lambda.min"))[-1],
vimp = as.matrix(coef(ridge_fit, s = "lambda.min"))[-1]
)
# random forest (MDI)
rf_fit <- ranger::ranger(
data = data,
formula = y ~ .,
importance = "impurity"
)
rf_vimp_mdi_df <- tibble::tibble(
var = names(rf_fit$variable.importance),
vimp = rf_fit$variable.importance
)
# random forest (permutation)
rf_fit <- ranger::ranger(
data = data,
formula = y ~ .,
importance = "permutation"
)
rf_vimp_perm_df <- tibble::tibble(
var = names(rf_fit$variable.importance),
vimp = rf_fit$variable.importance
)
# random forest (feature occlusion)
oob_errs <- c() # using out-of-bag error as the metric for simplicity (should generally use held-out test set)
for (j in names(rf_fit$variable.importance)) {
X_loco_j <- X |>
dplyr::select(-tidyselect::all_of(j))
rf_fit_j <- ranger::ranger(
data = cbind(y = y, X_loco_j),
formula = y ~ .
)
oob_errs[j] <- rf_fit_j$prediction.error
}
rf_vimp_loco_df <- tibble::tibble(
var = names(rf_fit$variable.importance),
vimp = oob_errs - rf_fit$prediction.error
)
# random forest (shap)
rf_fit <- ranger::ranger(
data = data,
formula = y ~ .
)
pred_fun <- function(object, newdata) {
predict(object, newdata)$predictions
}
shap_values <- fastshap::explain(
object = rf_fit,
X = X,
pred_wrapper = pred_fun,
nsim = 10
)
rf_vimp_shap_df <- as.data.frame(abs(shap_values)) |>
dplyr::summarise(
dplyr::across(
tidyselect::everything(),
~ mean(.x)
)
) |>
tidyr::pivot_longer(
cols = tidyselect::everything(),
names_to = "var",
values_to = "vimp"
)
vimp_df <- list(
Linear = lm_vimp_df,
LASSO = lasso_vimp_df,
Ridge = ridge_vimp_df,
`RF (MDI)` = rf_vimp_mdi_df,
`RF (permute)` = rf_vimp_perm_df,
`RF (SHAP)` = rf_vimp_shap_df,
`RF (LOCO)` = rf_vimp_loco_df
) |>
dplyr::bind_rows(.id = "method") |>
dplyr::mutate(
method = forcats::fct_inorder(method),
color = dplyr::case_when(
var == "V1" ~ "Signal1",
var == "V2" ~ "Signal2",
stringr::str_detect(var, "corr") ~ "Correlated",
TRUE ~ "Other"
),
var = forcats::fct_inorder(var)
)
plt <- vimp_df |>
ggplot2::ggplot() +
ggplot2::aes(x = var, y = vimp, fill = color) +
ggplot2::geom_bar(stat = "identity") +
ggplot2::facet_wrap(~ method, ncol = 1, scales = "free_y") +
ggplot2::labs(x = "Feature", y = "Importance", fill = "") +
ggplot2::scale_fill_manual(
values = c(
Signal1 = "dodgerblue",
Signal2 = "darkgreen",
Correlated = "orange",
Other = "gray"
)
) +
vthemes::theme_vmodern(
x_text_angle = TRUE,
size_preset = "large"
)
fig_width <- dplyr::case_when(
ncol(data) > 20 ~ 20,
TRUE ~ 10
)
vthemes::subchunkify(
plt, i = subchunk_idx, fig_height = 16, fig_width = fig_width
)
subchunk_idx <- subchunk_idx + 1
fit_ls[[sim_name]] <- list(
Linear = lm_fit,
LASSO = lasso_fit,
Ridge = ridge_fit,
`RF` = rf_fit
)
vimp_ls[[sim_name]] <- vimp_df
}Independent Features
Correlated Non-signal Features
Correlated Signal Features (1 signal)
Correlated Signal Features (many signal)
Correlated Features: Ozone data
We will next investigate these different feature importance methods using a real-world dataset, namely the “Ozone” dataset from the mlbench R package. Using this dataset, we aim to predict the ozone readings using various meteorological features such as temperature, wind speed, humidity, air pressure, and other related measurements.
data("Ozone", package = "mlbench")
# clean data
data <- Ozone |>
dplyr::select(
ozone = V4,
temperature = V8,
inversion_height = V10,
pressure = V11,
visibility = V13,
millibar_pressure_height = V5,
humidity = V7,
inversion_temperature = V12,
wind = V6
)
na_samples <- apply(data, 1, function(x) any(is.na(x)))
data <- data[!na_samples, ]
y <- data |>
dplyr::pull(ozone)
X <- data |>
dplyr::select(-ozone)
plt <- data |>
tidyr::pivot_longer(
cols = tidyselect::everything(),
names_to = "feature",
values_to = "value"
) |>
ggplot2::ggplot() +
ggplot2::aes(x = value) +
ggplot2::facet_wrap(~ feature, scales = "free") +
ggplot2::geom_histogram(bins = 30) +
vthemes::theme_vmodern()
# linear regression
cat("\n\n## Linear Regression\n\n")Linear Regression
LASSO
lasso_fit <- glmnet::cv.glmnet(
x = as.matrix(X),
y = y,
alpha = 1
)
lasso_vimp_df <- tibble::tibble(
var = rownames(coef(lasso_fit, s = "lambda.min"))[-1],
vimp = as.matrix(coef(lasso_fit, s = "lambda.min"))[-1]
)
plot(lasso_fit)
lasso_path_df <- as.data.frame(as.matrix(lasso_fit$glmnet.fit$beta)) |>
setNames(lasso_fit$lambda) |>
tibble::rownames_to_column("Variable") |>
tidyr::pivot_longer(
cols = -Variable,
names_to = "Lambda",
values_to = "Coefficient"
) |>
dplyr::mutate(
Lambda = as.numeric(Lambda)
)
lasso_path_plt <- lasso_path_df |>
ggplot2::ggplot() +
ggplot2::aes(
x = log(Lambda),
y = Coefficient,
color = Variable,
group = Variable
) +
ggplot2::geom_line(linewidth = 1) +
ggplot2::geom_hline(yintercept = 0, color = "black", linetype = "dashed") +
vthemes::theme_vmodern(size_preset = "large")
vthemes::subchunkify(
plotly::ggplotly(lasso_path_plt), i = subchunk_idx,
fig_height = 6, fig_width = 10
)Ridge
ridge_fit <- glmnet::cv.glmnet(
x = as.matrix(X),
y = y,
alpha = 0,
nfolds = 5
)
ridge_vimp_df <- tibble::tibble(
var = rownames(coef(ridge_fit, s = "lambda.min"))[-1],
vimp = as.matrix(coef(ridge_fit, s = "lambda.min"))[-1]
)
plot(ridge_fit)
ridge_path_df <- as.data.frame(as.matrix(ridge_fit$glmnet.fit$beta)) |>
setNames(ridge_fit$lambda) |>
tibble::rownames_to_column("Variable") |>
tidyr::pivot_longer(
cols = -Variable,
names_to = "Lambda",
values_to = "Coefficient"
) |>
dplyr::mutate(
Lambda = as.numeric(Lambda)
)
ridge_path_plt <- ridge_path_df |>
ggplot2::ggplot() +
ggplot2::aes(
x = log(Lambda),
y = Coefficient,
color = Variable,
group = Variable
) +
ggplot2::geom_line(linewidth = 1) +
ggplot2::geom_hline(yintercept = 0, color = "black", linetype = "dashed") +
vthemes::theme_vmodern(size_preset = "large")
vthemes::subchunkify(
plotly::ggplotly(ridge_path_plt), i = subchunk_idx,
fig_height = 6, fig_width = 10
)subchunk_idx <- subchunk_idx + 1
# random forest (MDI)
rf_fit <- ranger::ranger(
data = data,
formula = ozone ~ .,
importance = "impurity"
)
rf_vimp_mdi_df <- tibble::tibble(
var = names(rf_fit$variable.importance),
vimp = rf_fit$variable.importance
)
# random forest (permutation)
rf_fit <- ranger::ranger(
data = data,
formula = ozone ~ .,
importance = "permutation"
)
rf_vimp_perm_df <- tibble::tibble(
var = names(rf_fit$variable.importance),
vimp = rf_fit$variable.importance
)
# random forest (feature occlusion)
oob_errs <- c() # using out-of-bag error as the metric for simplicity (should generally use held-out test set)
for (j in names(rf_fit$variable.importance)) {
X_loco_j <- X |>
dplyr::select(-tidyselect::all_of(j))
rf_fit_j <- ranger::ranger(
data = cbind(y = y, X_loco_j),
formula = y ~ .
)
oob_errs[j] <- rf_fit_j$prediction.error
}
rf_vimp_loco_df <- tibble::tibble(
var = names(rf_fit$variable.importance),
vimp = oob_errs - rf_fit$prediction.error
)
# random forest (shap)
rf_fit <- ranger::ranger(
data = data,
formula = ozone ~ .
)
pred_fun <- function(object, newdata) {
predict(object, newdata)$predictions
}
shap_values <- fastshap::explain(
object = rf_fit,
X = X,
pred_wrapper = pred_fun,
nsim = 10
)
rf_vimp_shap_df <- as.data.frame(abs(shap_values)) |>
dplyr::summarise(
dplyr::across(
tidyselect::everything(),
~ mean(.x)
)
) |>
tidyr::pivot_longer(
cols = tidyselect::everything(),
names_to = "var",
values_to = "vimp"
)
cat("\n\n## Summary\n\n")Summary
vimp_df <- list(
Linear = lm_vimp_df,
LASSO = lasso_vimp_df,
Ridge = ridge_vimp_df,
`RF (MDI)` = rf_vimp_mdi_df,
`RF (permute)` = rf_vimp_perm_df,
`RF (SHAP)` = rf_vimp_shap_df,
`RF (LOCO)` = rf_vimp_loco_df
) |>
dplyr::bind_rows(.id = "method") |>
dplyr::mutate(
method = forcats::fct_inorder(method)
)
plt <- vimp_df |>
ggplot2::ggplot() +
ggplot2::aes(x = var, y = vimp) +
ggplot2::geom_bar(stat = "identity") +
ggplot2::facet_wrap(~ method, ncol = 1, scales = "free_y") +
ggplot2::labs(x = "Feature", y = "Importance", fill = "") +
vthemes::theme_vmodern(
x_text_angle = TRUE,
size_preset = "large"
)
vthemes::subchunkify(
# Plot the heatmap
corrplot::corrplot(
cor(X), method = "color", order = "hclust",
col = colorRampPalette(c("blue", "white", "red"))(15),
addCoef.col = "black", # Add correlation coefficients
tl.col = "black", tl.srt = 45 # Rotate text labels
),
i = subchunk_idx, fig_height = 10, fig_width = 10
)
subchunk_idx <- subchunk_idx + 1
vthemes::subchunkify(
plt, i = subchunk_idx, fig_height = 16, fig_width = 10
)
---
title: "Correlated Features"
author: "Tiffany Tang"
date: "`r Sys.Date()`"
output: vthemes::vmodern
---

```{r setup, include=FALSE}
knitr::opts_chunk$set(echo = TRUE)
set.seed(331)

subchunk_idx <- 1
```

# Correlated Features Simulation {.tabset .tabset-vmodern}

<div class="panel panel-default padded-panel">
We will first investigate how various feature importance methods treat correlated variables under different simulation scenarios.
</div>

```{r results = "asis"}
n <- 500
p <- 10
beta <- 1
noise_sd <- 1
data_ls <- list()
vimp_ls <- list()
fit_ls <- list()

# case 1: independent features
X <- as.data.frame(matrix(rnorm(n * p), n, p))
y <- X[, 1] * beta + X[, 2] * beta + rnorm(n, sd = noise_sd)
data_ls[["Independent Features"]] <- data.frame(y = y, X)

# case 2: correlated non-signal features
p_cor <- 100
rho <- 0.9
sig <- matrix(rho, p_cor, p_cor)
X_cor <- MASS::mvrnorm(n, mu = rep(0, p_cor), Sigma = sig)
data_ls[["Correlated Non-signal Features"]] <- dplyr::bind_cols(
  data.frame(y = y, X), 
  as.data.frame(X_cor) |> dplyr::rename_with(~ paste0("corr", .x))
)

# case 3: correlated signal features (one signal)
sig <- matrix(rho, p_cor + 1, p_cor + 1)
X_cor <- MASS::mvrnorm(n, mu = rep(0, p_cor + 1), Sigma = sig)
X[, 1] <- X_cor[, 1]
X_cor <- X_cor[, -1]
y <- X[, 1] * beta + X[, 2] * beta + rnorm(n, sd = noise_sd)
data_ls[["Correlated Signal Features (1 signal)"]] <- dplyr::bind_cols(
  data.frame(y = y, X), 
  as.data.frame(X_cor) |> dplyr::rename_with(~ paste0("corr", .x))
)

# case 4: correlated signal features (many signal)
y <- X[, 1] * beta + X[, 2] * beta + rowSums(X_cor[, 1:4] * beta) + rnorm(n, sd = noise_sd)
data_ls[["Correlated Signal Features (many signal)"]] <- dplyr::bind_cols(
  data.frame(y = y, X), 
  as.data.frame(X_cor) |> dplyr::rename_with(~ paste0("corr", .x))
)

for (sim_name in names(data_ls)) {
  cat(sprintf("\n\n## %s {.tabset .tabset-pills .tabset-square}\n\n", sim_name))
  
  data <- data_ls[[sim_name]]
  y <- data |>
    dplyr::pull(y)
  X <- data |> 
    dplyr::select(-y)
  
  # linear regression
  lm_fit <- lm(y ~ ., data = data)
  lm_vimp_df <- tibble::tibble(
    var = names(summary(lm_fit)$coefficients[-1, 1]),
    vimp = summary(lm_fit)$coefficients[-1, 1],
    se = summary(lm_fit)$coefficients[-1, 2]
  )
  
  # LASSO regression
  lasso_fit <- glmnet::cv.glmnet(
    x = as.matrix(X),
    y = y,
    alpha = 1, 
    nfolds = 5
  )
  lasso_vimp_df <- tibble::tibble(
    var = rownames(coef(lasso_fit, s = "lambda.min"))[-1],
    vimp = as.matrix(coef(lasso_fit, s = "lambda.min"))[-1]
  )
  
  # ridge regression
  ridge_fit <- glmnet::cv.glmnet(
    x = as.matrix(X),
    y = y,
    alpha = 0, 
    nfolds = 5
  )
  ridge_vimp_df <- tibble::tibble(
    var = rownames(coef(ridge_fit, s = "lambda.min"))[-1],
    vimp = as.matrix(coef(ridge_fit, s = "lambda.min"))[-1]
  )
  
  # random forest (MDI)
  rf_fit <- ranger::ranger(
    data = data,
    formula = y ~ .,
    importance = "impurity"
  )
  rf_vimp_mdi_df <- tibble::tibble(
    var = names(rf_fit$variable.importance),
    vimp = rf_fit$variable.importance
  )
  
  # random forest (permutation)
  rf_fit <- ranger::ranger(
    data = data,
    formula = y ~ .,
    importance = "permutation"
  )
  rf_vimp_perm_df <- tibble::tibble(
    var = names(rf_fit$variable.importance),
    vimp = rf_fit$variable.importance
  )
  
  # random forest (feature occlusion)
  oob_errs <- c()  # using out-of-bag error as the metric for simplicity (should generally use held-out test set)
  for (j in names(rf_fit$variable.importance)) {
    X_loco_j <- X |>
      dplyr::select(-tidyselect::all_of(j))
    rf_fit_j <- ranger::ranger(
      data = cbind(y = y, X_loco_j),
      formula = y ~ .
    )
    oob_errs[j] <- rf_fit_j$prediction.error
  }
  rf_vimp_loco_df <- tibble::tibble(
    var = names(rf_fit$variable.importance),
    vimp = oob_errs - rf_fit$prediction.error
  )
  
  # random forest (shap)
  rf_fit <- ranger::ranger(
    data = data,
    formula = y ~ .
  )
  pred_fun <- function(object, newdata) {
    predict(object, newdata)$predictions
  }
  shap_values <- fastshap::explain(
    object = rf_fit,
    X = X,
    pred_wrapper = pred_fun,
    nsim = 10
  )
  rf_vimp_shap_df <- as.data.frame(abs(shap_values)) |> 
    dplyr::summarise(
      dplyr::across(
        tidyselect::everything(),
        ~ mean(.x)
      )
    ) |>
    tidyr::pivot_longer(
      cols = tidyselect::everything(),
      names_to = "var",
      values_to = "vimp"
    )
  
  vimp_df <- list(
    Linear = lm_vimp_df,
    LASSO = lasso_vimp_df,
    Ridge = ridge_vimp_df,
    `RF (MDI)` = rf_vimp_mdi_df,
    `RF (permute)` = rf_vimp_perm_df,
    `RF (SHAP)` = rf_vimp_shap_df,
    `RF (LOCO)` = rf_vimp_loco_df
  ) |>
    dplyr::bind_rows(.id = "method") |> 
    dplyr::mutate(
      method = forcats::fct_inorder(method),
      color = dplyr::case_when(
        var == "V1" ~ "Signal1",
        var == "V2" ~ "Signal2",
        stringr::str_detect(var, "corr") ~ "Correlated",
        TRUE ~ "Other"
      ),
      var = forcats::fct_inorder(var)
    )
  
  plt <- vimp_df |> 
    ggplot2::ggplot() +
    ggplot2::aes(x = var, y = vimp, fill = color) +
    ggplot2::geom_bar(stat = "identity") +
    ggplot2::facet_wrap(~ method, ncol = 1, scales = "free_y") +
    ggplot2::labs(x = "Feature", y = "Importance", fill = "") +
    ggplot2::scale_fill_manual(
      values = c(
        Signal1 = "dodgerblue",
        Signal2 = "darkgreen",
        Correlated = "orange",
        Other = "gray"
      )
    ) +
    vthemes::theme_vmodern(
      x_text_angle = TRUE,
      size_preset = "large"
    )
  fig_width <- dplyr::case_when(
    ncol(data) > 20 ~ 20,
    TRUE ~ 10
  )
  vthemes::subchunkify(
    plt, i = subchunk_idx, fig_height = 16, fig_width = fig_width
  )
  subchunk_idx <- subchunk_idx + 1
  
  fit_ls[[sim_name]] <- list(
    Linear = lm_fit,
    LASSO = lasso_fit,
    Ridge = ridge_fit,
    `RF` = rf_fit
  )
  vimp_ls[[sim_name]] <- vimp_df
}
```

# Correlated Features: Ozone data {.tabset .tabset-vmodern}

<div class="panel panel-default padded-panel">
We will next investigate these different feature importance methods using a real-world dataset, namely the "Ozone" dataset from the `mlbench` R package. Using this dataset, we aim to predict the ozone readings using various meteorological features such as temperature, wind speed, humidity, air pressure, and other related measurements.
</div>

```{r results = "asis"}
data("Ozone", package = "mlbench")

# clean data
data <- Ozone |> 
  dplyr::select(
    ozone = V4,
    temperature = V8,
    inversion_height = V10,
    pressure = V11,
    visibility = V13,
    millibar_pressure_height = V5,
    humidity = V7,
    inversion_temperature = V12,
    wind = V6
  )
na_samples <- apply(data, 1, function(x) any(is.na(x)))
data <- data[!na_samples, ]

y <- data |>
  dplyr::pull(ozone)
X <- data |> 
  dplyr::select(-ozone)

plt <- data |> 
  tidyr::pivot_longer(
    cols = tidyselect::everything(), 
    names_to = "feature", 
    values_to = "value"
  ) |> 
  ggplot2::ggplot() +
  ggplot2::aes(x = value) +
  ggplot2::facet_wrap(~ feature, scales = "free") +
  ggplot2::geom_histogram(bins = 30) +
  vthemes::theme_vmodern()

# linear regression
cat("\n\n## Linear Regression\n\n")
lm_fit <- lm(ozone ~ ., data = data)
lm_vimp_df <- tibble::tibble(
  var = names(summary(lm_fit)$coefficients[-1, 1]),
  vimp = summary(lm_fit)$coefficients[-1, 1],
  se = summary(lm_fit)$coefficients[-1, 2]
)
broom::tidy(lm_fit) |> 
  vthemes::pretty_DT()

# LASSO regression
cat("\n\n## LASSO\n\n")
lasso_fit <- glmnet::cv.glmnet(
  x = as.matrix(X),
  y = y,
  alpha = 1
)
lasso_vimp_df <- tibble::tibble(
  var = rownames(coef(lasso_fit, s = "lambda.min"))[-1],
  vimp = as.matrix(coef(lasso_fit, s = "lambda.min"))[-1]
)
plot(lasso_fit)
lasso_path_df <- as.data.frame(as.matrix(lasso_fit$glmnet.fit$beta)) |>
  setNames(lasso_fit$lambda) |> 
  tibble::rownames_to_column("Variable") |> 
  tidyr::pivot_longer(
    cols = -Variable, 
    names_to = "Lambda", 
    values_to = "Coefficient"
  ) |> 
  dplyr::mutate(
    Lambda = as.numeric(Lambda)
  )
lasso_path_plt <- lasso_path_df |> 
  ggplot2::ggplot() +
  ggplot2::aes(
    x = log(Lambda),
    y = Coefficient,
    color = Variable,
    group = Variable
  ) +
  ggplot2::geom_line(linewidth = 1) +
  ggplot2::geom_hline(yintercept = 0, color = "black", linetype = "dashed") +
  vthemes::theme_vmodern(size_preset = "large")
vthemes::subchunkify(
  plotly::ggplotly(lasso_path_plt), i = subchunk_idx,
  fig_height = 6, fig_width = 10
)
subchunk_idx <- subchunk_idx + 1

# ridge regression
cat("\n\n## Ridge\n\n")
ridge_fit <- glmnet::cv.glmnet(
  x = as.matrix(X),
  y = y,
  alpha = 0, 
  nfolds = 5
)
ridge_vimp_df <- tibble::tibble(
  var = rownames(coef(ridge_fit, s = "lambda.min"))[-1],
  vimp = as.matrix(coef(ridge_fit, s = "lambda.min"))[-1]
)
plot(ridge_fit)
ridge_path_df <- as.data.frame(as.matrix(ridge_fit$glmnet.fit$beta)) |>
  setNames(ridge_fit$lambda) |> 
  tibble::rownames_to_column("Variable") |> 
  tidyr::pivot_longer(
    cols = -Variable, 
    names_to = "Lambda", 
    values_to = "Coefficient"
  ) |> 
  dplyr::mutate(
    Lambda = as.numeric(Lambda)
  )
ridge_path_plt <- ridge_path_df |> 
  ggplot2::ggplot() +
  ggplot2::aes(
    x = log(Lambda),
    y = Coefficient,
    color = Variable,
    group = Variable
  ) +
  ggplot2::geom_line(linewidth = 1) +
  ggplot2::geom_hline(yintercept = 0, color = "black", linetype = "dashed") +
  vthemes::theme_vmodern(size_preset = "large")
vthemes::subchunkify(
  plotly::ggplotly(ridge_path_plt), i = subchunk_idx,
  fig_height = 6, fig_width = 10
)
subchunk_idx <- subchunk_idx + 1

# random forest (MDI)
rf_fit <- ranger::ranger(
  data = data,
  formula = ozone ~ .,
  importance = "impurity"
)
rf_vimp_mdi_df <- tibble::tibble(
  var = names(rf_fit$variable.importance),
  vimp = rf_fit$variable.importance
)

# random forest (permutation)
rf_fit <- ranger::ranger(
  data = data,
  formula = ozone ~ .,
  importance = "permutation"
)
rf_vimp_perm_df <- tibble::tibble(
  var = names(rf_fit$variable.importance),
  vimp = rf_fit$variable.importance
)

# random forest (feature occlusion)
oob_errs <- c()  # using out-of-bag error as the metric for simplicity (should generally use held-out test set)
for (j in names(rf_fit$variable.importance)) {
  X_loco_j <- X |>
    dplyr::select(-tidyselect::all_of(j))
  rf_fit_j <- ranger::ranger(
    data = cbind(y = y, X_loco_j),
    formula = y ~ .
  )
  oob_errs[j] <- rf_fit_j$prediction.error
}
rf_vimp_loco_df <- tibble::tibble(
  var = names(rf_fit$variable.importance),
  vimp = oob_errs - rf_fit$prediction.error
)

# random forest (shap)
rf_fit <- ranger::ranger(
  data = data,
  formula = ozone ~ .
)
pred_fun <- function(object, newdata) {
  predict(object, newdata)$predictions
}
shap_values <- fastshap::explain(
  object = rf_fit,
  X = X,
  pred_wrapper = pred_fun,
  nsim = 10
)
rf_vimp_shap_df <- as.data.frame(abs(shap_values)) |> 
  dplyr::summarise(
    dplyr::across(
      tidyselect::everything(),
      ~ mean(.x)
    )
  ) |>
  tidyr::pivot_longer(
    cols = tidyselect::everything(),
    names_to = "var",
    values_to = "vimp"
  )

cat("\n\n## Summary\n\n")
vimp_df <- list(
  Linear = lm_vimp_df,
  LASSO = lasso_vimp_df,
  Ridge = ridge_vimp_df,
  `RF (MDI)` = rf_vimp_mdi_df,
  `RF (permute)` = rf_vimp_perm_df,
  `RF (SHAP)` = rf_vimp_shap_df,
  `RF (LOCO)` = rf_vimp_loco_df
) |>
  dplyr::bind_rows(.id = "method") |> 
  dplyr::mutate(
    method = forcats::fct_inorder(method)
  )

plt <- vimp_df |> 
  ggplot2::ggplot() +
  ggplot2::aes(x = var, y = vimp) +
  ggplot2::geom_bar(stat = "identity") +
  ggplot2::facet_wrap(~ method, ncol = 1, scales = "free_y") +
  ggplot2::labs(x = "Feature", y = "Importance", fill = "") +
  vthemes::theme_vmodern(
    x_text_angle = TRUE,
    size_preset = "large"
  )

vthemes::subchunkify(
  # Plot the heatmap
  corrplot::corrplot(
    cor(X), method = "color", order = "hclust",
    col = colorRampPalette(c("blue", "white", "red"))(15),
    addCoef.col = "black", # Add correlation coefficients
    tl.col = "black", tl.srt = 45 # Rotate text labels
  ),
  i = subchunk_idx, fig_height = 10, fig_width = 10
)
subchunk_idx <- subchunk_idx + 1
vthemes::subchunkify(
  plt, i = subchunk_idx, fig_height = 16, fig_width = 10
)
subchunk_idx <- subchunk_idx + 1
```


